Can you please tell me the origin of this formula?

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Discussion Overview

The discussion revolves around the origin and derivation of a specific formula related to the neutron diffusion equation, as presented in a book by Weston M. Stacey. Participants are exploring the relationships between the variables in the formula and their geometric interpretations.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant mentions finding the formula in a book on neutron diffusion, indicating its relevance to that topic.
  • Another participant questions the validity of the formula, suggesting that it may not hold true in general and seeks clarification on the relationships between the variables.
  • A subsequent post attempts to clarify the geometric interpretation of the angles involved, describing a triangle on a sphere and referencing standard geometric principles.

Areas of Agreement / Disagreement

Participants express differing views on the validity of the formula, with some seeking clarification and others providing interpretations. The discussion remains unresolved regarding the general applicability of the equation.

Contextual Notes

There are unresolved questions about the definitions and relationships of the variables involved in the formula, as well as the assumptions underlying its application.

Nafis Fuad
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I found this formula when I was studying neutron diffusion equation in Weston M. Stacey's book
Thanks in advance

cosβ=cosθx cosθ+sinθx sinθ cos(ψy−ψ)

Edited by moderator for clarity:
##\cos(\beta) = \cos(\theta_x)\cos(\theta) + \sin(\theta_x)\sin(\theta)\cos(\psi y - \psi)##
 
Last edited by a moderator:
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How is the second line related to the first one?
Where do these variables come from and how are they related? The equation is not true in general.
 
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Here it is
 

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##\psi - \psi_y## is the angle between the two planes of (one vector and x) and (the other vector and x).

We can imagine ##\beta##, ##\theta## and ##\theta_r## (as drawn) to form a triangle on a sphere with radius 1, with ##\psi - \psi_y## as angle between the last two. The problem is then standard geometry on a sphere, see e.g. Wikipedia.